Theorem pm5.71

Description: Theorem *5.71 of WhiteheadRussell p. 125. (Contributed by Roy F. Longton, 23-Jun-2005)

	Ref	Expression
Assertion	pm5.71	|- ( ( ps -> -. ch ) -> ( ( ( ph \/ ps ) /\ ch ) <-> ( ph /\ ch ) ) )

Proof

Step	Hyp	Ref	Expression
1		orel2	|- ( -. ps -> ( ( ph \/ ps ) -> ph ) )
2		orc	|- ( ph -> ( ph \/ ps ) )
3	1 2	impbid1	|- ( -. ps -> ( ( ph \/ ps ) <-> ph ) )
4	3	anbi1d	|- ( -. ps -> ( ( ( ph \/ ps ) /\ ch ) <-> ( ph /\ ch ) ) )
5		pm2.21	|- ( -. ch -> ( ch -> ( ( ph \/ ps ) <-> ph ) ) )
6	5	pm5.32rd	|- ( -. ch -> ( ( ( ph \/ ps ) /\ ch ) <-> ( ph /\ ch ) ) )
7	4 6	ja	|- ( ( ps -> -. ch ) -> ( ( ( ph \/ ps ) /\ ch ) <-> ( ph /\ ch ) ) )